Linear Difference Equations With Discrete Transform Methods
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Linear Difference Equations With Discrete Transform Methods
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Author : A.J. Jerri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Linear Difference Equations With Discrete Transform Methods written by A.J. Jerri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv ing, primarily, ordinary linear difference equations. Examples from various fields are presented clearly in the first chapter, then discussed along with their detailed solutions in Chapters 2-7. The book is in tended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the di rect use of the discrete Fourier transforms for solving boundary value problems associated with difference equations represents an added new feature compared to other existing books on the subject at this introductory level. This means that in addition to the familiar meth ods of solving difference equations that are covered in Chapter 3, this book emphasizes the use of discrete transforms. It is an attempt to introduce the methods and mechanics of discrete transforms for solv ing ordinary difference equations. The treatment closely parallels what many students have already learned about using the opera tional (integral) calculus of Laplace and Fourier transforms to solve differential equations. As in the continuous case, discrete operational methods may not solve problems that are intractable by other meth ods, but they can facilitate the solution of a large class of discrete initial and boundary value problems. Such operational methods, or what we shall term "operational sum calculus," may be extended eas ily to solve partial difference equations associated with initial and/or boundary value problems.
Difference Equations Second Edition
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Author : R Mickens
language : en
Publisher: CRC Press
Release Date : 1991-01-01
Difference Equations Second Edition written by R Mickens and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.
In recent years, the study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equations by finite-difference schemes, and the study of deterministic chaos. The second edition of Difference Equations: Theory and Applications provides a thorough listing of all major theorems along with proofs. The text treats the case of first-order difference equations in detail, using both analytical and geometrical methods. Both ordinary and partial difference equations are considered, along with a variety of special nonlinear forms for which exact solutions can be determined. Numerous worked examples and problems allow readers to fully understand the material in the text. They also give possible generalization of the theorems and application models. The text's expanded coverage of application helps readers appreciate the benefits of using difference equations in the modeling and analysis of "realistic" problems from a broad range of fields. The second edition presents, analyzes, and discusses a large number of applications from the mathematical, biological, physical, and social sciences. Discussions on perturbation methods and difference equation models of differential equation models of differential equations represent contributions by the author to the research literature. Reference to original literature show how the elementary models of the book can be extended to more realistic situations. Difference Equations, Second Edition gives readers a background in discrete mathematics that many workers in science-oriented industries need as part of their general scientific knowledge. With its minimal mathematical background requirements of general algebra and calculus, this unique volume will be used extensively by students and professional in science and technology, in areas such as applied mathematics, control theory, population science, economics, and electronic circuits, especially discrete signal processing.
Difference Equations
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Author : Walter G. Kelley
language : en
Publisher: Academic Press
Release Date : 2001
Difference Equations written by Walter G. Kelley and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics. Phase plane analysis for systems of two linear equations Use of equations of variation to approximate solutions Fundamental matrices and Floquet theory for periodic systems LaSalle invariance theorem Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory Appendix on the use of Mathematica for analyzing difference equaitons Exponential generating functions Many new examples and exercises
Linear Differential And Difference Equations
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Author : R. M. Johnson
language : en
Publisher: Elsevier
Release Date : 1997-06-01
Linear Differential And Difference Equations written by R. M. Johnson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-01 with Mathematics categories.
This text for advanced undergraduates and graduates reading applied mathematics, electrical, mechanical, or control engineering, employs block diagram notation to highlight comparable features of linear differential and difference equations, a unique feature found in no other book. The treatment of transform theory (Laplace transforms and z-transforms) encourages readers to think in terms of transfer functions, i.e. algebra rather than calculus. This contrives short-cuts whereby steady-state and transient solutions are determined from simple operations on the transfer functions. Employs block diagram notation to highlight comparable features of linear differential and difference equations The treatment of transform theory (Laplace transforms and z-transforms) encourages readers to think in terms of transfer functions, i.e. algebra rather than calculus
Discrete Transforms
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Author : J.M. Firth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discrete Transforms written by J.M. Firth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree course in which transform techniques will have a significant application. In other disciplines the readership will be past the second year undergraduate stage. In either case, the text is also intended for earlier graduates whose degree courses did not include this type of material and who now find themselves, in a professional capacity, requiring a knowledge of discrete transform methods.
Theory And Applications Of Linear Differential And Difference Equations
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Author : Roy Michael Johnson
language : en
Publisher: Ellis Horwood
Release Date : 1984
Theory And Applications Of Linear Differential And Difference Equations written by Roy Michael Johnson and has been published by Ellis Horwood this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Difference And Differential Equations With Applications In Queueing Theory
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Author : Aliakbar Montazer Haghighi
language : en
Publisher: John Wiley & Sons
Release Date : 2013-05-28
Difference And Differential Equations With Applications In Queueing Theory written by Aliakbar Montazer Haghighi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-28 with Technology & Engineering categories.
A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of topics that are used in stochastic processes, particularly in queueing theory, the book thoroughly discusses the relationship to systems of linear differential difference equations. The book demonstrates the applicability that queueing theory has in a variety of fields including telecommunications, traffic engineering, computing, and the design of factories, shops, offices, and hospitals. Along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform, Difference and Differential Equations with Applications in Queueing Theory provides: A discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models Applications in queue models whose solutions require differential difference equations and generating function methods Exercises at the end of each chapter along with select answers The book is an excellent resource for researchers and practitioners in applied mathematics, operations research, engineering, and industrial engineering, as well as a useful text for upper-undergraduate and graduate-level courses in applied mathematics, differential and difference equations, queueing theory, probability, and stochastic processes.
Signals And Linear Systems
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Author : Robert A. Gabel
language : en
Publisher: John Wiley & Sons
Release Date : 1991-01-16
Signals And Linear Systems written by Robert A. Gabel and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-16 with Science categories.
Unifies the various approaches used to characterize the interaction of signals with systems. Stresses their commonality, and contrasts difference/differential equation models, convolution, and state variable formulations in presenting continuous- and discrete-time systems. Transform methods are also discussed as they relate to corresponding time-domain techniques. This edition expands discussion of applications of the theoretical material in physical problems, enhancing students' ability to relate this material to design activities. Material on deconvolution has also been added to the time-domain and transform-domain treatments of discrete-time systems. Contains many examples and equations.
An Introduction To Fast Fourier Transform Methods For Partial Differential Equations With Applications
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Author : Morgan Pickering
language : en
Publisher: John Wiley & Sons
Release Date : 1986-11-28
An Introduction To Fast Fourier Transform Methods For Partial Differential Equations With Applications written by Morgan Pickering and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-11-28 with Mathematics categories.
Fast Fourier transform (FFT) methods are well established for solving certain types of partial differential equations (PDE). This book is written at an introductory level with the non-specialist user in mind. It first deals with basic ideas and algorithms which may be used to solve problems using simple geometries--the fast Fourier transform is employed and thorough details of the computations are given for a number of illustrative problems. The text proceeds to problems with irregular boundaries, using the capacity matrix approach, and also to more advanced PDE, for which fast solvers may be used as the basis for iterative methods. The use of a numerical Laplace transform technique for certain time-dependent problems is also covered. Throughout the book, the approach is designed to illustrate the essential ideas of the methods employed. References are given for further reading of more advanced or specialized topics.
An Introduction To Difference Equations
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Author : Saber Elaydi
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-29
An Introduction To Difference Equations written by Saber Elaydi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-29 with Mathematics categories.
A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics Contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations. Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems. Includes chapters on continued fractions, orthogonal polynomials and asymptotics. Lucid and transparent writing style